# The Atom

The atom is the smallest unit of matter that is composed of three sub-atomic particles: the proton, the neutron, and the electron. Protons and neutrons make up the nucleus of the atom, a dense and positively charged core, whereas the negatively charged electrons can be found around the nucleus in an electron cloud.

### The Structure of Atoms

An atom consists of a positively charged nucleus surrounded by one or more negatively charged particles called electrons. The number of protons found in the nucleus equals the number of electrons that surround it, giving the atom a neutral charge (neutrons have zero charge). Most of an atom’s mass is in its nucleus; the mass of an electron is only 1/1836 the mass of the lightest nucleus, that of hydrogen. Although the nucleus is heavy, it is small compared with the overall size of an atom.

The radius of a typical atom is around 1 to 2.5 angstroms (Å), whereas the radius of a nucleus is about 10-5 Å. If an atom were enlarged to the size of the earth, its nucleus would be only 200 feet in diameter and could easily fit inside a small football stadium.The nucleus of an atom contains protons and neutrons. Protons and neutrons have nearly equal masses, but they differ in charge. A neutron has no charge, whereas a proton has a positive charge that exactly balances the negative charge on an electron. Table 1 lists the charges of these three sub atomic particles, and gives their masses expressed in atomic mass units. The atomic mass unit (amu) is defined as exactly one-twelfth the mass of a carbon atom that has six protons and six neutrons in its nucleus. On this scale, protons and neutrons have masses that are close to, but not precisely, 1 u each. In fact, there are 6.022 x 1023 u in 1 gram. This number is known as Avogadro’s number, N. The number of protons in the nucleus of an atom is known as the atomic number, Z. It is the same as the number of electrons around the nucleus of the electrically-neutral atom. The mass number of an atom is equal to the total number of protons and neutrons.

 Particle Charge Mass (grams) Electrons -1 9.1094x10-28 Protons +1 1.6726x10-24 Neutrons 0 1.6749x10-24

Table 1: Charge and mass of three sub atomic particles

When two atoms are close enough to combine chemically and form chemical bonds with one another, each atom “sees” the outermost electrons of the other atom. These outer electrons, called valence electrons, are the most important factors in the chemical behavior of atoms. Both the neutron and the proton have key roles in the characteristics of an atom. The number of neutrons determine the type of isotope the element could be and the proton determines the number of electrons that surround its nucleus.

All atoms with the same atomic number exhibit the same chemical behaviors and are classified as the same chemical element. Each element has its own name and a one- or two-letter symbol (usually derived from the element’s English or Latin name). For example, the symbol for carbon is C, and the symbol for calcium is Ca. It is important to note that for elements with two letters, the first letter is capital and the second letter is lowercase. The symbol for sodium is Na—the first two letters of its Latin (and German) name, natriumto distinguish it from nitrogen, N, and sulfur, S.

Example

What is the atomic symbol for bromine, and what is its atomic number? Why is it incorrect to use the letter B? What other element preempts the symbol B? (Refer to the periodic table)

SOLUTION

Bromine’s atomic number is 35, and its symbol is Br; B is the symbol for boron

### Nucleus

The nucleus of an atom is comprised of protons and neutrons; it is therefore positively charged. The number of protons within the nucleus of a given atom is equal to the atomic number of the corresponding element, which can be found on the periodic table. For example, the atomic number of helium is two. Therefore, the number of protons is also two. The number of neutrons within the nucleus of a given atom can be found by subtracting the atomic number from the atomic mass. The mass number is the sum of protons and neutrons.

Atomic Mass Number = Number of Protons + Number of Neutrons

To find the number of neutrons, subtract the atomic number, the number of protons, from the mass number.

Notation of a specific element follows this format:

$$^A_Z {\rm E} ^c$$

where E is a specific element, A is mass number, Z is the atomic number, and C is the charge. For helium, the notation is as follows:

$$^4_2 {\rm He}$$

Helium has 2 protons, 2 neutrons and a charge of zero.

#### Isotopes

Atoms of the same element that have a different number of neutrons are known as isotopes. Most elements have several naturally occurring isotopes. The atomic mass of a particular element is equal to the average of the relative abundance of all its isotopes found in nature. For example, there are three naturally occurring isotopes of carbon: carbon-12, carbon-13, and carbon-14. Carbon-12 is the most common of these three, making up about 98.89% of all carbon, whereas carbon-13 has 1.11% natural abundance. Carbon-14 occurs rarely in nature. Atomic masses for other elements uses the carbon-12 scale as a reference. Early physicists assigned the atomic mass of 12 to the carbon-12 isotope (which is the most common carbon isotope) so that it would be easier to determine the atomic masses of other atoms. Using this information, we can determine the average atomic mass of carbon. (Use 13 for the approximate mass of carbon-13.)

average atomic mass = mass of carbon-12 x (% natural abundance/100) + mass of carbon-13 x (% natural abundance/100)

= 12 x .9889 + 13 x .0111 = 12.0111

Table 2 gives examples of common isotopes and their percent abundances in nature:

Table 2: Percent natural abundances of common isotopes.

 Element # of Neutrons Natural Abundance Hydrogen-1 0 99.985% Hydrogen-2 1 .015% Boron-10 5 19.900% Boron-11 6 80.100% Carbon-12 6 98.890% Carbon-13 7 1.110% Oxygen-16 8 99.762% Oxygen-17 9 .038% Oxygen-18 10 .200% Chlorine-35 18 75.770% Chlorine-37 20 24.230%

Example

How many protons, neutrons, and electrons are there in an atom of uranium-238? Write the symbol for this isotope.

SOLUTION

The atomic number of uranium (see periodic table) is 92, and the mass number of the isotope is 238. Therefore, it has 92 protons, 92 electrons, 146 neutrons (238 amu - 92 protons). Its symbol is $$^{238}_{92}{\rm U}$$ (or 238U).

The total mass of an atom is called its atomic weight, and this is approximately the sum of the masses of its constituent protons, neutrons, and electrons.  When protons, neutrons, and electrons combine to form an atom, some of their mass is converted to energy and is given off (this is the source of energy in nuclear fusion reactions; because the atom cannot be broken down into its fundamental particles unless the energy for the missing mass is supplied from outside it, this energy is called the binding energy of the nucleus).

Each isotope of an element is characterized by an atomic number (total number of protons), a mass number (total number of protons and neutrons), and an atomic weight (mass of atom in atomic mass units). Because the reduction in mass upon the formation of an atom is small, the mass number is usually the same as the atomic weight rounded to the nearest integer (for example, the atomic weight of chlorine-37 is 36.966, which is rounded to 37). If there are several isotopes of an element in nature, then the experimentally observed atomic weight (the natural atomic weight) is the weighted average of the isotope weights. The average is weighted according to the percent abundance of the isotopes. In general, all isotopes of an element have similar chemical properties. Their behaviors differ with regard to mass-sensitive properties such as diffusion rates.

Example: Magnesium

Magnesium (Mg) has three significant natural isotopes: 78.70% of all magnesium atoms have an atomic weight of 23.985 u, 10.13% have an atomic weight of 24.986 u, and 11.17% have an atomic weight of 25.983 u. How many protons and neutrons are present in each of these three isotopes? What are the symbols for each isotope? What is the weighted average of the atomic weights?

SOLUTION

There are 12 protons in each magnesium isotope. The isotope whose atomic weight is 23.985 u has a mass number of 24 (protons and neutrons), so 24 - 12 protons gives 12 neutrons. The symbol for this isotope is 24Mg. Similarly, the isotope whose atomic weight is 24.986 amu has a mass number of 25, 13 neutrons, and 25Mg as a symbol. The third isotope (25.983 amu) has a mass number of 26, 14 neutrons, and 26Mg as a symbol. We calculate the average atomic weight as follows:

(0.7870 x 23.985) + (0.1013 x 24.986) + (0.1117 x 25.983) = 24.31 u

Example: Boron

Boron has two naturally occurring isotopes, 10B and 11B. We know that 80.22% of its atoms are 11B, atomic weight 11.009 u. From the natural atomic weight given on the inside front cover, calculate the atomic weight of the 10B isotope.

SOLUTION

If 80.22% of all boron atoms are 11B, then 100.00 - 80.22 or 19.78% are the unknown isotope, because the percentage abundance of isotopes must add up to 100%. In the periodic table the atomic weight of boron is found to be 10.81 u. W represents the unknown atomic weight:

$\begin{eqnarray} (0.8022 \times 11.009) + (0.1978 \times W) &=& 10.81 {\rm u} \quad {\rm (natural~atomic~weight)} \\ W &=& \frac{10.81-8.831}{0.1978} \\ &=& 10.01 {\rm u} \end{eqnarray}$

### Electron Cloud

What appears to be a cloud of electrons surrounds the nucleus of an atom. The electron cloud serves as a model to help visualize the location of electrons in an atom. These electrons are held in place by their attraction to protons in the nucleus. This attraction is known as an electromagnetic force. Electrons move around the nucleus very quickly, creating the image of a cloud; however, they actually form electron shells. Each electron shell can hold a certain amount of electrons. The first shell holds two electrons, and subsequent shells hold eight electrons (the movement of electrons is discussed in Unit IV). The number of electrons in a given atom is equal to the number of protons in that atom. However, units of the same element can have different numbers of electrons. Such units are known as ions. Atoms that lose one or more electrons become positively charged and are called cations. Cations are smaller than the original atom due to the loss of an electron. Examples of cations include Ca2+ and Al3(note: An H+ cation is simply a proton). Atoms can also gain electrons, forming a negative ion known as an anion. Anions are bigger that the original atoms due to electron gain. Examples of anions include Cl- and O2-. Although some elements may only gain one electron, some atoms can gain up to four electrons.

### Problems

1. Complete the chart below.

 Element Protons Neutrons Electrons Charge $$^3_2 {\rm He}$$ 1 2 0 $$^{129}_{53} {\rm I} ^-$$ 53 54 -1 $$^{30}_{14} {\rm Si}$$ 14 18 18 0 $$^9_4 {\rm Be} ^{2+}$$ 2 3 3 0 $$^{80}_{35} {\rm Br} ^+$$ 35 45 -1 $$^{27}_{13} {\rm Al} ^{3+}$$ 13 10 $$^{35}_{17} {\rm Cl} ^-$$ 18 18 -1 $$^{15}_7 {\rm N}$$ 7 7 82 126 +2 $$^{10}_5 {\rm B}$$

2. Boron has two naturally occurring isotopes, boron-10 and boron-11, with the masses of 10.013 g and 11.009 g, respectively. What is the average atomic mass of boron?

3. What is the mass of chlorine-37, if the mass of chlorine-35 is 34.969 g and the atomic mass of chlorine is 35.453 g? (Hint: Refer to table.1.)

4. For the atom 196Pt4, indicate the number of protons, neutrons and electrons.

5. Write the notation for an atom containing 24 protons, 28 neutrons and 21 electrons.

1.

 Element Protons Neutrons Electrons Charge $$^3_2 {\rm He}$$ 2 1 2 0 $$^{129}_{53} {\rm I} ^-$$ 53 76 54 -1 $$^{30}_{14} {\rm Si}$$ 14 16 14 0 $$^{36}_{18} {\rm Ar}$$ 18 18 18 0 $$^9_4 {\rm Be} ^{2+}$$ 4 5 2 2+ $$^6_3 {\rm Li}$$ 3 3 3 0 $$^{80}_{35} {\rm Br} ^+$$ 35 45 36 -1 $$^{27}_{13} {\rm Al} ^{3+}$$ 13 14 10 3+ $$^{35}_{17} {\rm Cl} ^-$$ 17 18 18 -1 $$^{15}_7 {\rm N}$$ 7 8 7 0 $$^{208}_{82} {\rm Pb} ^{2+}$$ 82 126 80 2+ $$^{10}_5 {\rm B}$$ 5 5 5 0

2. Referring to table.1, the percent natural abundance of boron-10 is 19.9% and the percent natural abundance of boron-11 is 80.1%. Multiply the given masses by their respective percents (in decimal form) to find the average.

(10.0129 x .199) + (11.00931 x .801) = 10.811

The average atomic mass of boron is 10.811 g.

3. If we refer to table.1, we find the percent natural abundance of chlorine-35 is 75.77% and the percent natural abundance for chlorine-37 is 24.23. Using the same general formula as in the previous problem, solve for the mass of chlorine-37 (represented by n)/;

(34.969 x .7577) + (n x .2423) = 35.453

26.496 + .2423n = 35.453

.2423n= 8.957

n = 36.967

The mass of chlorine-37 is 36.967 g.

4. Number of protons = 78.

Number of neutrons = 118.

Number of electrons = 74.

5. 52Cr3+